Transformations Unit Test Part 1
1. What is a transformation in mathematics?
A transformation is a change in the position, size, or shape of a geometric figure. This change can include translations (slides), rotations (turns), reflections (flips), and dilations (changes in size).
2. Explain the difference between a translation and a reflection.
A translation is a transformation where a figure is moved from one location to another without changing its size or shape. This can be done horizontally, vertically, or in any other direction. A reflection, on the other hand, is a transformation that flips a figure over a line or a point, creating a mirror image.
3. Describe how to perform a rotation of a figure on a coordinate plane.
To perform a rotation of a figure on a coordinate plane, you need to choose a center of rotation and an angle of rotation. The figure is then rotated around the center according to the angle specified. Each point on the figure is moved the same distance and direction as every other point, creating a new position for the figure while maintaining its size and shape.
4. What is a dilation in mathematics?
A dilation is a transformation that changes the size of a figure while keeping its shape the same. This can involve enlarging or shrinking the figure by a certain scale factor. Dilations are performed using a center of dilation and a scale factor to determine the new size of the figure.
5. How can you determine if two figures are congruent after a transformation has been applied?
Two figures are congruent if they have the same size and shape. To determine if two figures are congruent after a transformation, you can compare their corresponding angles and side lengths to see if they match up. If all angles and side lengths are equal, then the figures are congruent.